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A Treatise on Solid Geometry, by P. Frost and J. Wolstenholme

A Treatise on Solid Geometry, by P. Frost and J. Wolstenholme


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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1863 Excerpt: ...the two equations of the line; hence if the equations be x = mz + a, y = nz + b, m, n, a, b must be functions of one parameter, which by its variation gives rise to different positions of the generating line. The shortest distance between two consecutive lines of the system is Am Ab--An Aa and similarly for An, Aa, and Ab;.. Am Ab--An Aa = dm db--dn da, +-(dm db + db dm--dn da--da dn), + terms of the following order higher than the third, the denominator is of the first order, and if dm db--dn da be not zero, the numerator is of the second order, but if dm db--dnda = 0 always, we have also dm db + db dm--dn da--da dn = 0; or the numerator is of the fourth or higher order. Hence the truth of the proposition which is due to M. Bouquet. Tangent planes touching along a curve line. 302. We have seen (Art. 287) that, when a plane intersects a surface, at every point of the curve of intersection, through which Q an arbitrary line drawn in the plane passes through two coincident points, the plane is a tangent plane to the surface, or such a point is a multiple point on the surface. If the curve of intersection consist of two or more coincident lines, this will occur at every point of such curves, hence, either the plane will be a tangent plane to the surface at every point of such multiple curve, or will contain a multiple line on the surface. Conversely, if a tangent plane touch along a curve line such a curve line will be a multiple line on the tangent plane. Thus in the case of the anchor ring, the plane which touches the anchor ring at every point has for its curve of intersection the two circles coincident in LKH; also the tangent plane to a cone contains two generating lines which ultimately coincide, and is therefore a tangent plane at every point of the gen...


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Product Details
  • ISBN-13: 9781130284713
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 104
  • Spine Width: 6 mm
  • Width: 189 mm
  • ISBN-10: 1130284719
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 200 gr

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